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Academy11+

11+ Maths · Topic explained

Volume

How many sugar cubes fit in a box?

The big idea

Volume is how much space a 3D shape takes up, counted in cubes.

Picture it

Like packing sugar cubes into a box, one layer at a time.

Key words

volume
The space inside a solid shape.
cubic centimetre (cm³)
A cube 1 cm on each edge.
cuboid rule
Volume = length × width × height.
capacity
How much a container holds, often in litres.

Worked examples

  1. 1Warm-up

    Find the volume of a cube with edges of 3 cm.

    • 3 × 3 × 3 = 27 cm³
  2. 211+ standard

    Find the volume of a cuboid 5 cm long, 4 cm wide and 3 cm high.

    • One layer: 5 × 4 = 20 cubes
    • 3 layers: 20 × 3 = 60 cm³
  3. 311+ standard

    A fish tank is 20 cm by 10 cm by 10 cm. How many litres of water does it hold?

    • 20 × 10 × 10 = 2000 cm³
    • 1 litre = 1000 cm³
    • 2000 cm³ = 2 litres
  4. 411+ standard

    A box has a volume of 72 cm³. Its base is 4 cm by 3 cm. How tall is it?

    • Base: 4 × 3 = 12 cubes a layer
    • 72 ÷ 12 = 6 cm tall

The common mistake

The mistake

Volume of a 5 by 4 by 3 cuboid = 5 + 4 + 3 = 12 cm³.

Instead

Multiply: 5 × 4 × 3 = 60 cm³.

Why: Volume counts every cube inside: rows times columns times layers.

Where it comes up in the 11+

Cubes and cuboids, missing lengths, and litres (1 litre = 1000 cm³).

The video

Video coming soon

We're making a short video that explains volume step by step. Until then, everything it covers is on this page.

Free printable

Volume worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. What is the volume of a cube with edges of 2 cm?

    • 6 cm³
    • 8 cm³
    • 4 cm³
    • 12 cm³
    Show the answer

    8 cm³

    2 × 2 × 2 = 8.

  2. 2. What is the volume of a box 10 cm by 5 cm by 2 cm?

    • 17 cm³
    • 100 cm³
    • 50 cm³
    • 80 cm³
    Show the answer

    100 cm³

    10 × 5 × 2 = 100.

  3. 3. How many cubic centimetres are there in 1 litre?

    • 10
    • 100
    • 1000
    • 10 000
    Show the answer

    1000

    1 litre = 1000 ml = 1000 cm³.